Problem: Solve for $x$ : $4x^2 - 24x + 32 = 0$
Solution: Dividing both sides by $4$ gives: $ x^2 {-6}x + {8} = 0 $ The coefficient on the $x$ term is $-6$ and the constant term is $8$ , so we need to find two numbers that add up to $-6$ and multiply to $8$ The two numbers $-2$ and $-4$ satisfy both conditions: $ {-2} + {-4} = {-6} $ $ {-2} \times {-4} = {8} $ $(x {-2}) (x {-4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -2) (x -4) = 0$ $x - 2 = 0$ or $x - 4 = 0$ Thus, $x = 2$ and $x = 4$ are the solutions.